Issue 51

F. Clementi et alii, Frattura ed Integrità Strutturale, 51 (2020) 313-335; DOI: 10.3221/IGF-ESIS.51.24 321 and   ,  T loc free m free v q v W I           H . Finally, the Non-Linear Gauss Seidel method allows to solve the contact problem. Therefore, between the discrete element methods, there is the NSCD method, which is characterized by three main points: (i) the non-smooth contact laws are directly integrated inside it, (ii) an implicit integration scheme is implemented and (iii) structural damping are not considered into it. Furthermore, the NSCD method requires some simplifications on the building of models. First of all, the bodies are assumed perfectly rigid and, secondly, the contact laws between blocks are determined by the Signorini's impenetrability condition and by the dry-friction à la Coulomb . Thus, these relations on the contacts involve the perfectly plastic impacts, hence without bounces as a consequence, i.e., a null value of the restitution coefficient in the Newton law. According to it, there is the main advantage of the limited computational complexity derived by the simple modelling of the impacts. Afterward, another relevant benefit due to the perfectly plastic impact is related to the dissipation of energy, which explains the damages of the material and the micro-cracks of the stones after the collisions and, additionally, supports the numerical integration and its stability from a computational point of view. Finally, in these models, the dissipated energy is determined by the involvement of the friction and it does not consider the damping effects, which instead are essential for the continuum models. Figure 9 : Views of the North façade (a), East façade (b), South façade (c), West façade (d) of the numerical model with steel chains of the civic clock tower of Amatrice (Rieti, Italy) with the NSCD method. T HE CIVIC BELL TOWER ’ S NUMERICAL MODEL he modelling of the Amatrice civic clock tower aims to build the geometry by means of the discontinuous approach, assigning appropriate mechanical properties to the model, thus to appreciate all the possible dynamic behaviour of the masonry under the influence of the friction coefficient between the blocks. For this reason, the existing configuration of the Amatrice tower was taken into account, with its actual dimensions and the past interventions still present on the masonry structure seriously damaged by the Central Italy seismic sequence of 2016. Thus two numerical models are formed by rigid blocks of different dimensions and regular convex shapes considering (Fig. T